Operator Theory, Free Harmonic Analysis, and Related Problems

Indiana University, Bloomington IN

Investigators

Abstract

ABSTRACT DMS-0070459 The proposed research involves the study of operators and their invariant subspaces, and some problems arising in the theory of free random variables. The problems on invariant subspaces will focus on the structure and classification results which can in special cases be inferred from the combinatorics of Young tableaux. Problems in free probability will concern the weak laws for arbitrary arrays, and the study of multiplicative stability. The finer harmonic analysis of free convolutions will also be studied. The work proposed here is mostly of a theoretical nature, and it is intended to clarify some (sometimes unexpected) connections between objects studied in different areas (such as operator theory, complex analysis, and combinatorial analysis). This kind of work does often have connections with more applied areas. The one specific applied area closely related to the operator theory is control theory and optimization where operators have indeed found rather striking applications.